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10th December 2023, 09:47 PM #1
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A mathematical puzzle to solve...
Circle A is 1/3 of the radius of Circle B.Capture.JPG
If circle A revolves its circumference around the circumference of Circle B (which remains staionary), how many times will Circle A rotate on its journey? The circumference of a circle is 2 * Pi * r or Pi * Dia.
The same question, slightly rephrased, is posed in this picture (where Circle B remains stationary):
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10th December 2023, 10:17 PM #2
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The circumference of A must be 1/3 of B, so three revolutions. My backup answer is avocado green
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10th December 2023, 10:20 PM #3
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??? Three ???
Using pi multiplied by D to get the circumference of each circle and that r = R/3 the two equations seem to cancel each other out with only “3” being left…
… but it is late, I’m practically in bed and I did that totally in my head so I’m probably wrong…Nothing succeeds like a budgie without a beak.
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10th December 2023, 10:34 PM #4
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I've heard this exact problem being discussed recently. Perfect timing!
The SAT Question Everyone Got Wrong - YouTube
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10th December 2023, 10:36 PM #5
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4. A does an extra revolution around its own axis of rotation in addition to its own circumference around B's circumference.
Circle Revolutions and the Coin Rotation Paradox
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10th December 2023, 11:01 PM #6
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super! Thanks, I never quite had a good explanation of a sidereal day but now I see it’s linked to this problem, makes it much easier to explain
Originally Posted by taz01
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10th December 2023, 11:22 PM #7
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That's where I saw it today. Thought y'all might like a puzzle. Originally Posted by taz01
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11th December 2023, 12:35 AM #8
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Just a footnote to this puzzle: one of the comments under the video said:
"Thinking about this yesterday and I realized the extra rotation becomes intuitive if you shrink the large circle down to a point, and rotate around that. Even though the diameter of the circle it's rotating around is zero, the "small" circle still has to make a full rotation to return to its starting point."
That's a great explanation!
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